A rectangular piece of tin is three times as long as it is wide. Squares 2.5 cm on a side are cut out of each ?
let x ≡ length, y ≡ width, x = 3y V = x y h .................................... note that h = 2.5 = 5/2 (3y - 5) (y - 5) 5/2 = 728 ............ subtract 5 cm for the corners 3y² - 20y + 25 = 1456/5 3y² - 20y = 1331/5 y² - 20/3 y = 1331/15 (y - 20/6)² = 4493/45 y = √(4493/45) + 10/3........ discard the (-) root x = 3√(4493/45) + 10 ........ x = 3y Answer: √(4493/45) + 10/3 cm x 3√(4493/45) + 10 cm .. ≈ 13.33 cm x 39.98 cm Verify: (13.33 - 5) (39.98 - 5) (2.5) ≈ 728
How many squares of side 5cm can be adjusted in a rectangular box of size 25*15*10 cm?
If the 5x5 squares are 2-dimensional, and the box is 3-dimensional, you could theoretically fit an infinite number of squares into the box.